You will need to remove the plastic and dig over properly in order to plant, and that means removing the wood chips/mulch. If the chips are not fresh wood, its worth keeping them somewhere to replace direct on the soil after planting, with no liner beneath, because they will break down and improve the soil over time, but if they are fresh wood, best to leave them in a pile somewhere to rot down for a year or so before placing back on the soil. If the liner beneath is not actually just plastic sheeting but instead is proper landscape fabric/weed liner, you will still need to roll it back to prepare the soil, but you could actually replace it after planting, cutting holes where you have planted, and cover with chips afterwards to keep weed growth down and help retain moisture in the soil.
I would suggest you only remove the chips and liner in areas you are ready to work on, leaving the rest in situ till later; sometimes, a liner with chips on top might mean the previous owner did it to stop growth from things which are present in the soil and which may then regrow when you remove it all, and some of this growth might be undesirable, such as pernicious weeds. This is why you'll need to dig over an area, both to break up any soil compaction and to see if there is root material or anything already in the soil that is currently not visible, and which you may need to clear out before replanting. It's also wise to incorporate some composted materials into the soil to improve fertility as you work, so things like spent mushroom compost, leaf mould, composted manure, anything like that you can get hold of.